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id	challengeType	title	forumTopicId
5900f5411000cf542c510054	5	Problem 468: Smooth divisors of binomial coefficients	302143

Description

An integer is called B-smooth if none of its prime factors is greater than B.

Let SB(n) be the largest B-smooth divisor of n. Examples: S1(10) = 1 S4(2100) = 12 S17(2496144) = 5712

Define F(n) = ∑1≤B≤n ∑0≤r≤n SB(C(n,r)). Here, C(n,r) denotes the binomial coefficient. Examples: F(11) = 3132 F(1 111) mod 1 000 000 993 = 706036312 F(111 111) mod 1 000 000 993 = 22156169

Find F(11 111 111) mod 1 000 000 993.

Instructions

Tests

tests:
  - text: <code>euler468()</code> should return 852950321.
    testString: assert.strictEqual(euler468(), 852950321);

Challenge Seed

function euler468() {
  // Good luck!
  return true;
}

euler468();

Solution

// solution required

1.1 KiB Raw Blame History